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<a href="_hypervolume_contribution3_d_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno">    1</span><span class="comment">/*!</span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno">    2</span><span class="comment"> *</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno">    3</span><span class="comment"> * \author      O.Krause, T. Glasmachers</span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno">    4</span><span class="comment"> * \date        2014-2016</span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno">    5</span><span class="comment"> *</span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno">    6</span><span class="comment"> *</span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno">    7</span><span class="comment"> * \par Copyright 1995-2017 Shark Development Team</span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno">    8</span><span class="comment"> * </span></div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno">    9</span><span class="comment"> * &lt;BR&gt;&lt;HR&gt;</span></div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno">   10</span><span class="comment"> * This file is part of Shark.</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno">   11</span><span class="comment"> * &lt;https://shark-ml.github.io/Shark/&gt;</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno">   12</span><span class="comment"> * </span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno">   13</span><span class="comment"> * Shark is free software: you can redistribute it and/or modify</span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno">   14</span><span class="comment"> * it under the terms of the GNU Lesser General Public License as published </span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno">   15</span><span class="comment"> * by the Free Software Foundation, either version 3 of the License, or</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno">   16</span><span class="comment"> * (at your option) any later version.</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno">   17</span><span class="comment"> * </span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno">   18</span><span class="comment"> * Shark is distributed in the hope that it will be useful,</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span><span class="comment"> * but WITHOUT ANY WARRANTY; without even the implied warranty of</span></div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span><span class="comment"> * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the</span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span><span class="comment"> * GNU Lesser General Public License for more details.</span></div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span><span class="comment"> * </span></div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span><span class="comment"> * You should have received a copy of the GNU Lesser General Public License</span></div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span><span class="comment"> * along with Shark.  If not, see &lt;http://www.gnu.org/licenses/&gt;.</span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno">   25</span><span class="comment"> *</span></div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span><span class="comment"> */</span></div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span><span class="preprocessor">#ifndef SHARK_ALGORITHMS_DIRECTSEARCH_HYPERVOLUME_CONTRIBUTION_3D_H</span></div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span><span class="preprocessor">#define SHARK_ALGORITHMS_DIRECTSEARCH_HYPERVOLUME_CONTRIBUTION_3D_H</span></div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span> </div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span><span class="preprocessor">#include &lt;<a class="code" href="_base_8h.html">shark/LinAlg/Base.h</a>&gt;</span></div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span><span class="preprocessor">#include &lt;<a class="code" href="_key_value_pair_8h.html">shark/Core/utility/KeyValuePair.h</a>&gt;</span></div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span> </div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span><span class="preprocessor">#include &lt;algorithm&gt;</span></div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span><span class="preprocessor">#include &lt;vector&gt;</span></div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span><span class="preprocessor">#include &lt;deque&gt;</span></div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span><span class="preprocessor">#include &lt;set&gt;</span></div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span><span class="preprocessor">#include &lt;utility&gt;</span></div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span> </div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceshark.html" title="AbstractMultiObjectiveOptimizer.">shark</a> {<span class="comment"></span></div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span><span class="comment">/// \brief Finds the hypervolume contribution for points in 3DD</span></div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span><span class="comment">///</span></div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span><span class="comment">/// The algorithm sweeps ascending through the z-direction and keeps track of</span></div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span><span class="comment">/// of the current cut through the volume at a given z-value.</span></div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span><span class="comment">/// the cut is partitioned in boxes representing parts of the hypervolume</span></div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span><span class="comment">/// that is not hared with any other point. thus the sum of</span></div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span><span class="comment">/// the volume of all boxes belonging to a point is making</span></div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span><span class="comment">/// up its hypervolume.</span></div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span><span class="comment">///</span></div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span><span class="comment">/// The algorithm runs in O(n log(n)) time.</span></div>
<div class="foldopen" id="foldopen00050" data-start="{" data-end="};">
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"><a class="line" href="structshark_1_1_hypervolume_contribution3_d.html">   50</a></span><span class="comment"></span><span class="keyword">struct </span><a class="code hl_struct" href="structshark_1_1_hypervolume_contribution3_d.html" title="Finds the hypervolume contribution for points in 3DD.">HypervolumeContribution3D</a> {</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span><span class="keyword">private</span>:</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>    <span class="keyword">struct </span>Point{</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>        Point(){}</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span> </div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>        Point(<span class="keywordtype">double</span> f1, <span class="keywordtype">double</span> f2, <span class="keywordtype">double</span> f3, std::size_t index)</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>        : f1(f1)</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>        , f2(f2)</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>        , f3(f3)</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>        , index(index)</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>        {}</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>            </div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>        <span class="keywordtype">bool</span> operator&lt;(Point <span class="keyword">const</span>&amp; rhs)<span class="keyword"> const</span>{<span class="comment">//sort by x1 coordinate</span></div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>            <span class="keywordflow">return</span> f1 &lt; rhs.f1;</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>        }</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>        </div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>        <span class="keyword">template</span>&lt;<span class="keyword">class</span> S&gt;</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>        <span class="keyword">friend</span> <a class="code hl_define" href="_r_v_e_a_8h.html#a9d2dc49fb253b5729d15f1cba751ed76">S</a>&amp; <a class="code hl_function" href="namespaceshark.html#a09ff8eea9690a4f7c082d545d1ba997b">operator&lt;&lt;</a>(<a class="code hl_define" href="_r_v_e_a_8h.html#a9d2dc49fb253b5729d15f1cba751ed76">S</a>&amp; s,Point <span class="keyword">const</span>&amp; p){</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>            s&lt;&lt;<span class="stringliteral">&quot;(&quot;</span>&lt;&lt;p.f1&lt;&lt;<span class="stringliteral">&quot;,&quot;</span>&lt;&lt;p.f2&lt;&lt;<span class="stringliteral">&quot;,&quot;</span>&lt;&lt;p.f3&lt;&lt;<span class="stringliteral">&quot;)&quot;</span>;</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>            <span class="keywordflow">return</span> s;</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>        }</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>        </div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>        <span class="keywordtype">double</span> f1;</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>        <span class="keywordtype">double</span> f2;</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>        <span class="keywordtype">double</span> f3;</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>        std::size_t index;</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>    };</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>    <span class="comment"></span></div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span><span class="comment">    ///\brief Box representing part of the hypervolume of a point</span></div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span><span class="comment">    /// by convention a unclosed box has lower.f3=upper.f3 and when its</span></div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span><span class="comment">    /// upper boundary is found, it is set to the right value and its volume</span></div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span><span class="comment">    /// is computed.</span></div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span><span class="comment">    /// Boxes are stored in boxlists sorted ascending by x-coordinate.</span></div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span><span class="comment"></span>    <span class="keyword">struct </span>Box{</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>        Point lower;</div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>        Point upper;</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>        </div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>        <span class="keywordtype">double</span> volume()<span class="keyword">const</span>{</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>            <span class="keywordflow">return</span> (upper.f1-lower.f1)*(upper.f2-lower.f2)*(upper.f3-lower.f3);</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>        }</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>    };</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>    </div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span><span class="comment"></span> </div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span><span class="comment">    /// \brief Updates the volumes of the first nondominated neighbour of the new point to the right</span></div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span><span class="comment">    /// The volume of the newly added point intersects with boxes of its neighbour in the front.</span></div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span><span class="comment">    /// Thus we remove all boxes intersecting with this one, compute their volume and add it to</span></div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span><span class="comment">    /// the total volume of right. The boxes are replaced by one new box representing the non-intersecting</span></div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span><span class="comment">    /// contribution that is still to be determined.</span></div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span><span class="comment"></span>    <span class="keywordtype">double</span> cutBoxesOnTheRight(std::deque&lt;Box&gt;&amp; rightList, Point <span class="keyword">const</span>&amp; point, Point <span class="keyword">const</span>&amp; right)<span class="keyword">const</span>{</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>        <span class="keywordflow">if</span>(rightList.empty()) <span class="keywordflow">return</span> 0;<span class="comment">//nothing to do</span></div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>        </div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>        <span class="keywordtype">double</span> addedContribution = 0;</div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>        <span class="keywordtype">double</span> xright = right.f1;</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>        <span class="comment">//iterate through all partly covered boxes</span></div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>        <span class="keywordflow">while</span>(!rightList.empty()){</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>            Box&amp; b = rightList.front();</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>            <span class="comment">//if the box is not partially covered, we are done as by sorting all other boxes have smaller y-value</span></div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>            <span class="keywordflow">if</span>(b.upper.f2 &lt;= point.f2)</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>                <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>                </div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>            <span class="comment">//add volume of box</span></div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>            b.upper.f3 = point.f3;</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>            addedContribution += b.volume();</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>            xright = b.upper.f1;</div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>            rightList.pop_front();</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>        }</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>        <span class="keywordflow">if</span>(xright != right.f1){<span class="comment">//if we removed a box</span></div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>            <span class="comment">//in the last step, we have removed boxes that were only partially</span></div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>            <span class="comment">//covered. replace them by a box that covers their area</span></div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>            Box rightBox;</div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>            rightBox.lower.f1 = right.f1;</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>            rightBox.lower.f2 = right.f2;</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>            rightBox.lower.f3 = point.f3;</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>            rightBox.upper.f1 = xright;</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>            rightBox.upper.f2 = point.f2;</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>            rightBox.upper.f3 = point.f3;</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>            <span class="comment">//upper.f3 remains unspecified until the box is completed</span></div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>            rightList.push_front(rightBox);</div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>        }</div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>        <span class="keywordflow">return</span> addedContribution;</div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>    }</div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>    <span class="comment"></span></div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span><span class="comment">    /// \brief Updates the volumes of the first neighbour of the new point to the left</span></div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span><span class="comment">    /// The volume of the newly added point intersects with boxes of its neighbours in the front.</span></div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span><span class="comment">    /// On the left side, we can even completely dominate whole boxes which are removed.</span></div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span><span class="comment">    /// Otherwise, the boxes are intersected with the volume of the new point and shrunk to the remainder</span></div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span><span class="comment">    /// This method removes the volume of boxes removed that way.</span></div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span><span class="comment"></span>    <span class="keywordtype">double</span> cutBoxesOnTheLeft(std::deque&lt;Box&gt;&amp; leftList, Point <span class="keyword">const</span>&amp; point)<span class="keyword">const</span>{</div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>        <span class="keywordtype">double</span> addedContribution = 0;</div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>        <span class="keywordflow">while</span>(!leftList.empty()){</div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>            Box&amp; b= leftList.back();</div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>            <span class="keywordflow">if</span>(point.f1 &lt; b.lower.f1 ){<span class="comment">//is the box completely covered?</span></div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>                b.upper.f3 = point.f3;</div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>                addedContribution += b.volume();</div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>                leftList.pop_back();</div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>            }<span class="keywordflow">else</span> <span class="keywordflow">if</span>(point.f1 &lt; b.upper.f1 ){<span class="comment">//is the box partly covered?</span></div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>                <span class="comment">//Add contribution</span></div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>                b.upper.f3 = point.f3;</div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>                addedContribution += b.volume();</div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>                <span class="comment">//replace box by the new box that starts from the height of p</span></div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span>                b.upper.f1 = point.f1;</div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>                b.lower.f3 = point.f3;</div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>                <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span>            }<span class="keywordflow">else</span>{</div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>                <span class="keywordflow">break</span>;<span class="comment">//uncovered</span></div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>            }</div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>        }</div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>        <span class="keywordflow">return</span> addedContribution;</div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>    }</div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>    </div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>    std::vector&lt;KeyValuePair&lt;double,std::size_t&gt; &gt; allContributions(std::vector&lt;Point&gt; <span class="keyword">const</span>&amp; points)<span class="keyword">const</span>{</div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>        </div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>        std::size_t n = points.size();</div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>        <span class="comment">//for every point we have a list of boxes that make up its contribution, L in the paper.</span></div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>        <span class="comment">//the list stores the boxes ordered by x-value + one additional (empty) list for the added corner points</span></div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>        std::vector&lt;std::deque&lt;Box&gt; &gt; boxlists(n+1);</div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>        <span class="comment">//contributions are accumulated here for every point</span></div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>        std::vector&lt;KeyValuePair&lt;double,std::size_t&gt; &gt; contributions(n+1,<a class="code hl_function" href="namespaceshark.html#a45f02945ba29df1104c012e614d38591" title="Creates a KeyValuePair.">makeKeyValuePair</a>(0.0,1));</div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span>        <span class="keywordflow">for</span>(std::size_t i = 0; i != n; ++i){</div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>            contributions[i].value = points[i].index;</div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>        }</div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>        </div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>        <span class="comment">//The tree stores values ordered by x-value and is our xy front.</span></div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>        <span class="comment">// even though we store 3D points, the third component is not relevant</span></div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>        <span class="comment">// thus the values are also ordered by y-component.</span></div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>        std::multiset&lt;Point&gt; xyFront;</div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>        <span class="comment">//insert points indiating the reference frame, required for setting up the boxes.</span></div>
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span>        <span class="comment">//The 0 stands for the reference point (0,0) in x-y coordinate</span></div>
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span>        <span class="comment">//the -inf ensures that the point never becomes dominated</span></div>
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span>        <span class="keywordtype">double</span> inf = std::numeric_limits&lt;double&gt;::max();<span class="comment">//inf can be more costly to work with!</span></div>
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>        xyFront.insert(Point(-inf,0,-inf,n));</div>
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span>        xyFront.insert(Point(0,-inf,-inf,n));</div>
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span>        </div>
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>        <span class="comment">//main loop</span></div>
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>        <span class="keywordflow">for</span>(std::size_t i = 0; i != n; ++i){</div>
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span>            Point <span class="keyword">const</span>&amp; point = points[i];</div>
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>            </div>
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>            <span class="comment">//position of the point with next smaller x-value in the front</span></div>
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>            <span class="keyword">auto</span> left = xyFront.lower_bound(point);<span class="comment">//gives larger or equal          </span></div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>            --left;<span class="comment">//first smaller element</span></div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>            </div>
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span>            <span class="comment">//check if the new point is dominated</span></div>
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span>            <span class="keywordflow">if</span>(left-&gt;f2 &lt; point.f2)</div>
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>                <span class="keywordflow">continue</span>;</div>
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>            </div>
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>            <span class="comment">//find the indizes of all points dominated by the new point</span></div>
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>            <span class="comment">//and find the position of the next nondominated neighbour</span></div>
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>            <span class="comment">//with larger x-value</span></div>
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>            std::vector&lt;std::size_t&gt; dominatedPoints;</div>
<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>            <span class="keyword">auto</span> right= left; ++right;</div>
<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>            <span class="keywordflow">while</span>((*right).f2 &gt; point.f2){</div>
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>                dominatedPoints.push_back(right-&gt;index);</div>
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span>                ++right;</div>
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span>            }</div>
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span>            </div>
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno">  209</span>            </div>
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno">  210</span>            <span class="comment">//erase all dominated points from the front</span></div>
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno">  211</span>            xyFront.erase(std::next(left),right);</div>
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno">  212</span>            </div>
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno">  213</span>            <span class="comment">//add point to the front</span></div>
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno">  214</span>            xyFront.insert(Point(point.f1,point.f2,point.f3,i));</div>
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno">  215</span>            <span class="comment">//reorder dominated points so that the largest x-values are at the front</span></div>
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno">  216</span>            std::reverse(dominatedPoints.begin(),dominatedPoints.end());</div>
<div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span>            </div>
<div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span>            </div>
<div class="line"><a id="l00219" name="l00219"></a><span class="lineno">  219</span>            <span class="comment">//cut and remove neighbouring boxes</span></div>
<div class="line"><a id="l00220" name="l00220"></a><span class="lineno">  220</span>            contributions[left-&gt;index].key += cutBoxesOnTheLeft(boxlists[left-&gt;index],point);</div>
<div class="line"><a id="l00221" name="l00221"></a><span class="lineno">  221</span>            contributions[right-&gt;index].key += cutBoxesOnTheRight(boxlists[right-&gt;index],point,*right);</div>
<div class="line"><a id="l00222" name="l00222"></a><span class="lineno">  222</span>            </div>
<div class="line"><a id="l00223" name="l00223"></a><span class="lineno">  223</span>            <span class="comment">//Remove dominated points with their boxes</span></div>
<div class="line"><a id="l00224" name="l00224"></a><span class="lineno">  224</span>            <span class="comment">//and create new boxes for the new point</span></div>
<div class="line"><a id="l00225" name="l00225"></a><span class="lineno">  225</span>            <span class="keywordtype">double</span> xright = right-&gt;f1;</div>
<div class="line"><a id="l00226" name="l00226"></a><span class="lineno">  226</span>            <span class="keywordflow">for</span>(std::size_t domIndex:dominatedPoints){</div>
<div class="line"><a id="l00227" name="l00227"></a><span class="lineno">  227</span>                Point dominated = points[domIndex];</div>
<div class="line"><a id="l00228" name="l00228"></a><span class="lineno">  228</span>                <span class="keyword">auto</span>&amp; domList = boxlists[domIndex];</div>
<div class="line"><a id="l00229" name="l00229"></a><span class="lineno">  229</span>                <span class="keywordflow">for</span>(Box&amp; b:domList){</div>
<div class="line"><a id="l00230" name="l00230"></a><span class="lineno">  230</span>                    b.upper.f3 = point.f3;</div>
<div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span>                    contributions[domIndex].key += b.volume();</div>
<div class="line"><a id="l00232" name="l00232"></a><span class="lineno">  232</span>                }</div>
<div class="line"><a id="l00233" name="l00233"></a><span class="lineno">  233</span>                Box leftBox;</div>
<div class="line"><a id="l00234" name="l00234"></a><span class="lineno">  234</span>                leftBox.lower.f1 = dominated.f1;</div>
<div class="line"><a id="l00235" name="l00235"></a><span class="lineno">  235</span>                leftBox.lower.f2 = point.f2;</div>
<div class="line"><a id="l00236" name="l00236"></a><span class="lineno">  236</span>                leftBox.lower.f3 = point.f3;</div>
<div class="line"><a id="l00237" name="l00237"></a><span class="lineno">  237</span>                </div>
<div class="line"><a id="l00238" name="l00238"></a><span class="lineno">  238</span>                leftBox.upper.f1 = xright;</div>
<div class="line"><a id="l00239" name="l00239"></a><span class="lineno">  239</span>                leftBox.upper.f2 = dominated.f2;</div>
<div class="line"><a id="l00240" name="l00240"></a><span class="lineno">  240</span>                leftBox.upper.f3 = leftBox.lower.f3;</div>
<div class="line"><a id="l00241" name="l00241"></a><span class="lineno">  241</span>                <span class="comment">//upper.f3 remains unspecified until the box is completed</span></div>
<div class="line"><a id="l00242" name="l00242"></a><span class="lineno">  242</span>                boxlists[i].push_front(leftBox);</div>
<div class="line"><a id="l00243" name="l00243"></a><span class="lineno">  243</span>                </div>
<div class="line"><a id="l00244" name="l00244"></a><span class="lineno">  244</span>                xright = dominated.f1;</div>
<div class="line"><a id="l00245" name="l00245"></a><span class="lineno">  245</span>            }</div>
<div class="line"><a id="l00246" name="l00246"></a><span class="lineno">  246</span>            <span class="comment">//Add the new box created by this point</span></div>
<div class="line"><a id="l00247" name="l00247"></a><span class="lineno">  247</span>            Box newBox;</div>
<div class="line"><a id="l00248" name="l00248"></a><span class="lineno">  248</span>            newBox.lower.f1 = point.f1;</div>
<div class="line"><a id="l00249" name="l00249"></a><span class="lineno">  249</span>            newBox.lower.f2 = point.f2;</div>
<div class="line"><a id="l00250" name="l00250"></a><span class="lineno">  250</span>            newBox.lower.f3 = point.f3;</div>
<div class="line"><a id="l00251" name="l00251"></a><span class="lineno">  251</span>            newBox.upper.f1 = xright;</div>
<div class="line"><a id="l00252" name="l00252"></a><span class="lineno">  252</span>            newBox.upper.f2 = left-&gt;f2;</div>
<div class="line"><a id="l00253" name="l00253"></a><span class="lineno">  253</span>            newBox.upper.f3 = newBox.lower.f3;</div>
<div class="line"><a id="l00254" name="l00254"></a><span class="lineno">  254</span>            boxlists[i].push_front(newBox);</div>
<div class="line"><a id="l00255" name="l00255"></a><span class="lineno">  255</span>        }</div>
<div class="line"><a id="l00256" name="l00256"></a><span class="lineno">  256</span>        </div>
<div class="line"><a id="l00257" name="l00257"></a><span class="lineno">  257</span>        <span class="comment">//go through the front and close all remaining boxes</span></div>
<div class="line"><a id="l00258" name="l00258"></a><span class="lineno">  258</span>        <span class="keywordflow">for</span>(Point <span class="keyword">const</span>&amp; p: xyFront){</div>
<div class="line"><a id="l00259" name="l00259"></a><span class="lineno">  259</span>            std::size_t index = p.index;</div>
<div class="line"><a id="l00260" name="l00260"></a><span class="lineno">  260</span>            <span class="keywordflow">for</span>(Box &amp; b: boxlists[index]){</div>
<div class="line"><a id="l00261" name="l00261"></a><span class="lineno">  261</span>                b.upper.f3  = 0.0;</div>
<div class="line"><a id="l00262" name="l00262"></a><span class="lineno">  262</span>                contributions[index].key +=b.volume();</div>
<div class="line"><a id="l00263" name="l00263"></a><span class="lineno">  263</span>            }</div>
<div class="line"><a id="l00264" name="l00264"></a><span class="lineno">  264</span>        }</div>
<div class="line"><a id="l00265" name="l00265"></a><span class="lineno">  265</span>        </div>
<div class="line"><a id="l00266" name="l00266"></a><span class="lineno">  266</span>        <span class="comment">//finally sort contributions descending and return it</span></div>
<div class="line"><a id="l00267" name="l00267"></a><span class="lineno">  267</span>        contributions.pop_back();<span class="comment">//remove the superfluous last element</span></div>
<div class="line"><a id="l00268" name="l00268"></a><span class="lineno">  268</span>        std::sort(contributions.begin(),contributions.end());</div>
<div class="line"><a id="l00269" name="l00269"></a><span class="lineno">  269</span>        </div>
<div class="line"><a id="l00270" name="l00270"></a><span class="lineno">  270</span>        <span class="keywordflow">return</span> contributions;</div>
<div class="line"><a id="l00271" name="l00271"></a><span class="lineno">  271</span>    }</div>
<div class="line"><a id="l00272" name="l00272"></a><span class="lineno">  272</span>    </div>
<div class="line"><a id="l00273" name="l00273"></a><span class="lineno">  273</span><span class="keyword">public</span>:<span class="comment"></span></div>
<div class="line"><a id="l00274" name="l00274"></a><span class="lineno">  274</span><span class="comment">    /// \brief Returns the index of the points with smallest contribution as well as their contribution.</span></div>
<div class="line"><a id="l00275" name="l00275"></a><span class="lineno">  275</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00276" name="l00276"></a><span class="lineno">  276</span><span class="comment">    /// \param [in] points The set \f$S\f$ of points from which to select the smallest contributor.</span></div>
<div class="line"><a id="l00277" name="l00277"></a><span class="lineno">  277</span><span class="comment">    /// \param [in] k The number of points to select.</span></div>
<div class="line"><a id="l00278" name="l00278"></a><span class="lineno">  278</span><span class="comment">    /// \param [in] ref The reference Point\f$\vec{r} \in \mathbb{R}^2\f$ for the hypervolume calculation, needs to fulfill: \f$ \forall s \in S: s \preceq \vec{r}\f$.</span></div>
<div class="line"><a id="l00279" name="l00279"></a><span class="lineno">  279</span><span class="comment"></span>    <span class="keyword">template</span>&lt;<span class="keyword">class</span> Set, <span class="keyword">typename</span> VectorType&gt;</div>
<div class="foldopen" id="foldopen00280" data-start="{" data-end="}">
<div class="line"><a id="l00280" name="l00280"></a><span class="lineno"><a class="line" href="structshark_1_1_hypervolume_contribution3_d.html#ac4d761c1d24708031664aff96129c043">  280</a></span>    std::vector&lt;KeyValuePair&lt;double,std::size_t&gt; &gt; <a class="code hl_function" href="structshark_1_1_hypervolume_contribution3_d.html#ac4d761c1d24708031664aff96129c043" title="Returns the index of the points with smallest contribution as well as their contribution.">smallest</a>(Set <span class="keyword">const</span>&amp; points, std::size_t k, <a class="code hl_typedef" href="_c_svm_linear_8cpp.html#ab106d665148183a2dc94dcf8716c9203">VectorType</a> <span class="keyword">const</span>&amp; ref)<span class="keyword">const</span>{</div>
<div class="line"><a id="l00281" name="l00281"></a><span class="lineno">  281</span>        <a class="code hl_define" href="_exception_8h.html#adce1f80097c69010f5eab2618fa2e971">SHARK_RUNTIME_CHECK</a>(points.size() &gt;= k, <span class="stringliteral">&quot;There must be at least k points in the set&quot;</span>);</div>
<div class="line"><a id="l00282" name="l00282"></a><span class="lineno">  282</span>        std::vector&lt;Point&gt; front;</div>
<div class="line"><a id="l00283" name="l00283"></a><span class="lineno">  283</span>        <span class="keywordflow">for</span>(std::size_t i = 0; i != points.size(); ++i){</div>
<div class="line"><a id="l00284" name="l00284"></a><span class="lineno">  284</span>            front.emplace_back(points[i](0)-ref(0),points[i](1)-ref(1),points[i](2)-ref(2),i);</div>
<div class="line"><a id="l00285" name="l00285"></a><span class="lineno">  285</span>        }</div>
<div class="line"><a id="l00286" name="l00286"></a><span class="lineno">  286</span>        std::sort(</div>
<div class="line"><a id="l00287" name="l00287"></a><span class="lineno">  287</span>            front.begin(),front.end(),</div>
<div class="line"><a id="l00288" name="l00288"></a><span class="lineno">  288</span>            [](Point <span class="keyword">const</span>&amp; lhs, Point <span class="keyword">const</span>&amp; rhs){</div>
<div class="line"><a id="l00289" name="l00289"></a><span class="lineno">  289</span>                return lhs.f3 &lt; rhs.f3;</div>
<div class="line"><a id="l00290" name="l00290"></a><span class="lineno">  290</span>            }</div>
<div class="line"><a id="l00291" name="l00291"></a><span class="lineno">  291</span>        );</div>
<div class="line"><a id="l00292" name="l00292"></a><span class="lineno">  292</span>        </div>
<div class="line"><a id="l00293" name="l00293"></a><span class="lineno">  293</span>        <span class="keyword">auto</span> result = allContributions(front);</div>
<div class="line"><a id="l00294" name="l00294"></a><span class="lineno">  294</span>        result.erase(result.begin()+k,result.end());</div>
<div class="line"><a id="l00295" name="l00295"></a><span class="lineno">  295</span>        <span class="keywordflow">return</span> result;</div>
<div class="line"><a id="l00296" name="l00296"></a><span class="lineno">  296</span>    }</div>
</div>
<div class="line"><a id="l00297" name="l00297"></a><span class="lineno">  297</span>    <span class="comment"></span></div>
<div class="line"><a id="l00298" name="l00298"></a><span class="lineno">  298</span><span class="comment">    /// \brief Returns the index of the points with smallest contribution as well as their contribution.</span></div>
<div class="line"><a id="l00299" name="l00299"></a><span class="lineno">  299</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00300" name="l00300"></a><span class="lineno">  300</span><span class="comment">    /// As no reference point is given, the extremum points can not be computed and are never selected.</span></div>
<div class="line"><a id="l00301" name="l00301"></a><span class="lineno">  301</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00302" name="l00302"></a><span class="lineno">  302</span><span class="comment">    /// \param [in] points The set \f$S\f$ of points from which to select the smallest contributor.</span></div>
<div class="line"><a id="l00303" name="l00303"></a><span class="lineno">  303</span><span class="comment">    /// \param [in] k The number of points to select.</span></div>
<div class="line"><a id="l00304" name="l00304"></a><span class="lineno">  304</span><span class="comment"></span>    <span class="keyword">template</span>&lt;<span class="keyword">class</span> Set&gt;</div>
<div class="foldopen" id="foldopen00305" data-start="{" data-end="}">
<div class="line"><a id="l00305" name="l00305"></a><span class="lineno"><a class="line" href="structshark_1_1_hypervolume_contribution3_d.html#ad35f30562f9b12e8e85b9f4a268d39c3">  305</a></span>    std::vector&lt;KeyValuePair&lt;double,std::size_t&gt; &gt; <a class="code hl_function" href="structshark_1_1_hypervolume_contribution3_d.html#ad35f30562f9b12e8e85b9f4a268d39c3" title="Returns the index of the points with smallest contribution as well as their contribution.">smallest</a>(Set <span class="keyword">const</span>&amp; points, std::size_t k)<span class="keyword">const</span>{</div>
<div class="line"><a id="l00306" name="l00306"></a><span class="lineno">  306</span>        <a class="code hl_define" href="_exception_8h.html#adce1f80097c69010f5eab2618fa2e971">SHARK_RUNTIME_CHECK</a>(points.size() &gt;= k, <span class="stringliteral">&quot;There must be at least k points in the set&quot;</span>);</div>
<div class="line"><a id="l00307" name="l00307"></a><span class="lineno">  307</span>        <span class="comment">//reference point computation, and obtain the indizes of the extremum elements</span></div>
<div class="line"><a id="l00308" name="l00308"></a><span class="lineno">  308</span>        std::size_t minIndex[]={0,0,0};</div>
<div class="line"><a id="l00309" name="l00309"></a><span class="lineno">  309</span>        <span class="keywordtype">double</span> minVal[]={points[0](0),points[0](1),points[0](2)};</div>
<div class="line"><a id="l00310" name="l00310"></a><span class="lineno">  310</span>        <span class="keywordtype">double</span> ref[]={points[0](0),points[0](1),points[0](2)};</div>
<div class="line"><a id="l00311" name="l00311"></a><span class="lineno">  311</span>        <span class="keywordflow">for</span>(std::size_t i = 0; i != points.size(); ++i){</div>
<div class="line"><a id="l00312" name="l00312"></a><span class="lineno">  312</span>            <span class="keywordflow">for</span>(std::size_t j = 0; j != 3; ++j){</div>
<div class="line"><a id="l00313" name="l00313"></a><span class="lineno">  313</span>                <span class="keywordflow">if</span>(points[i](j)&lt; minVal[j]){</div>
<div class="line"><a id="l00314" name="l00314"></a><span class="lineno">  314</span>                    minVal[j] = points[i](j);</div>
<div class="line"><a id="l00315" name="l00315"></a><span class="lineno">  315</span>                    minIndex[j]=i;</div>
<div class="line"><a id="l00316" name="l00316"></a><span class="lineno">  316</span>                }</div>
<div class="line"><a id="l00317" name="l00317"></a><span class="lineno">  317</span>                ref[j] = std::max(ref[j],points[i](j));</div>
<div class="line"><a id="l00318" name="l00318"></a><span class="lineno">  318</span>            }</div>
<div class="line"><a id="l00319" name="l00319"></a><span class="lineno">  319</span>        }</div>
<div class="line"><a id="l00320" name="l00320"></a><span class="lineno">  320</span>        </div>
<div class="line"><a id="l00321" name="l00321"></a><span class="lineno">  321</span>        </div>
<div class="line"><a id="l00322" name="l00322"></a><span class="lineno">  322</span>        std::vector&lt;Point&gt; front;</div>
<div class="line"><a id="l00323" name="l00323"></a><span class="lineno">  323</span>        <span class="keywordflow">for</span>(std::size_t i = 0; i != points.size(); ++i){</div>
<div class="line"><a id="l00324" name="l00324"></a><span class="lineno">  324</span>            front.emplace_back(points[i](0)-ref[0],points[i](1)-ref[1],points[i](2)-ref[2],i);</div>
<div class="line"><a id="l00325" name="l00325"></a><span class="lineno">  325</span>        }</div>
<div class="line"><a id="l00326" name="l00326"></a><span class="lineno">  326</span>        std::sort(</div>
<div class="line"><a id="l00327" name="l00327"></a><span class="lineno">  327</span>            front.begin(),front.end(),</div>
<div class="line"><a id="l00328" name="l00328"></a><span class="lineno">  328</span>            [](Point <span class="keyword">const</span>&amp; lhs, Point <span class="keyword">const</span>&amp; rhs){</div>
<div class="line"><a id="l00329" name="l00329"></a><span class="lineno">  329</span>                return lhs.f3 &lt; rhs.f3;</div>
<div class="line"><a id="l00330" name="l00330"></a><span class="lineno">  330</span>            }</div>
<div class="line"><a id="l00331" name="l00331"></a><span class="lineno">  331</span>        );</div>
<div class="line"><a id="l00332" name="l00332"></a><span class="lineno">  332</span>        </div>
<div class="line"><a id="l00333" name="l00333"></a><span class="lineno">  333</span>        <span class="keyword">auto</span> result = allContributions(front);</div>
<div class="line"><a id="l00334" name="l00334"></a><span class="lineno">  334</span>        <span class="keywordflow">for</span>(std::size_t j = 0; j != 3; ++j){</div>
<div class="line"><a id="l00335" name="l00335"></a><span class="lineno">  335</span>            <span class="keyword">auto</span> pos = std::find_if(</div>
<div class="line"><a id="l00336" name="l00336"></a><span class="lineno">  336</span>                result.begin(),result.end(),</div>
<div class="line"><a id="l00337" name="l00337"></a><span class="lineno">  337</span>                [&amp;](<a class="code hl_struct" href="structshark_1_1_key_value_pair.html" title="Represents a Key-Value-Pair similar std::pair which is strictly ordered by it&#39;s key.">KeyValuePair&lt;double,std::size_t&gt;</a> <span class="keyword">const</span>&amp; p){</div>
<div class="line"><a id="l00338" name="l00338"></a><span class="lineno">  338</span>                    return p.value == minIndex[j];</div>
<div class="line"><a id="l00339" name="l00339"></a><span class="lineno">  339</span>                }</div>
<div class="line"><a id="l00340" name="l00340"></a><span class="lineno">  340</span>            );</div>
<div class="line"><a id="l00341" name="l00341"></a><span class="lineno">  341</span>            <span class="keywordflow">if</span>(pos != result.end())</div>
<div class="line"><a id="l00342" name="l00342"></a><span class="lineno">  342</span>                result.erase(pos);</div>
<div class="line"><a id="l00343" name="l00343"></a><span class="lineno">  343</span>        }</div>
<div class="line"><a id="l00344" name="l00344"></a><span class="lineno">  344</span>        result.erase(result.begin()+k,result.end());</div>
<div class="line"><a id="l00345" name="l00345"></a><span class="lineno">  345</span>        <span class="keywordflow">return</span> result;</div>
<div class="line"><a id="l00346" name="l00346"></a><span class="lineno">  346</span>    }</div>
</div>
<div class="line"><a id="l00347" name="l00347"></a><span class="lineno">  347</span> </div>
<div class="line"><a id="l00348" name="l00348"></a><span class="lineno">  348</span>    <span class="comment"></span></div>
<div class="line"><a id="l00349" name="l00349"></a><span class="lineno">  349</span><span class="comment">    /// \brief Returns the index of the points with largest contribution as well as their contribution.</span></div>
<div class="line"><a id="l00350" name="l00350"></a><span class="lineno">  350</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00351" name="l00351"></a><span class="lineno">  351</span><span class="comment">    /// \param [in] points The set \f$S\f$ of points from which to select the largest contributor.</span></div>
<div class="line"><a id="l00352" name="l00352"></a><span class="lineno">  352</span><span class="comment">    /// \param [in] k The number of points to select.</span></div>
<div class="line"><a id="l00353" name="l00353"></a><span class="lineno">  353</span><span class="comment">    /// \param [in] ref The reference Point\f$\vec{r} \in \mathbb{R}^2\f$ for the hypervolume calculation, needs to fulfill: \f$ \forall s \in S: s \preceq \vec{r}\f$.</span></div>
<div class="line"><a id="l00354" name="l00354"></a><span class="lineno">  354</span><span class="comment"></span>    <span class="keyword">template</span>&lt;<span class="keyword">class</span> Set, <span class="keyword">typename</span> VectorType&gt;</div>
<div class="foldopen" id="foldopen00355" data-start="{" data-end="}">
<div class="line"><a id="l00355" name="l00355"></a><span class="lineno"><a class="line" href="structshark_1_1_hypervolume_contribution3_d.html#a21b543685d2c16e733c932f8ca4f41d9">  355</a></span>    std::vector&lt;KeyValuePair&lt;double,std::size_t&gt; &gt; <a class="code hl_function" href="structshark_1_1_hypervolume_contribution3_d.html#a21b543685d2c16e733c932f8ca4f41d9" title="Returns the index of the points with largest contribution as well as their contribution.">largest</a>(Set <span class="keyword">const</span>&amp; points, std::size_t k, <a class="code hl_typedef" href="_c_svm_linear_8cpp.html#ab106d665148183a2dc94dcf8716c9203">VectorType</a> <span class="keyword">const</span>&amp; ref)<span class="keyword">const</span>{</div>
<div class="line"><a id="l00356" name="l00356"></a><span class="lineno">  356</span>        std::vector&lt;Point&gt; front;</div>
<div class="line"><a id="l00357" name="l00357"></a><span class="lineno">  357</span>        <span class="keywordflow">for</span>(std::size_t i = 0; i != points.size(); ++i){</div>
<div class="line"><a id="l00358" name="l00358"></a><span class="lineno">  358</span>            front.emplace_back(points[i](0)-ref(0),points[i](1)-ref(1),points[i](2)-ref(2),i);</div>
<div class="line"><a id="l00359" name="l00359"></a><span class="lineno">  359</span>        }</div>
<div class="line"><a id="l00360" name="l00360"></a><span class="lineno">  360</span>        std::sort(</div>
<div class="line"><a id="l00361" name="l00361"></a><span class="lineno">  361</span>            front.begin(),front.end(),</div>
<div class="line"><a id="l00362" name="l00362"></a><span class="lineno">  362</span>            [](Point <span class="keyword">const</span>&amp; lhs, Point <span class="keyword">const</span>&amp; rhs){</div>
<div class="line"><a id="l00363" name="l00363"></a><span class="lineno">  363</span>                return lhs.f3 &lt; rhs.f3;</div>
<div class="line"><a id="l00364" name="l00364"></a><span class="lineno">  364</span>            }</div>
<div class="line"><a id="l00365" name="l00365"></a><span class="lineno">  365</span>        );</div>
<div class="line"><a id="l00366" name="l00366"></a><span class="lineno">  366</span>        </div>
<div class="line"><a id="l00367" name="l00367"></a><span class="lineno">  367</span>        <span class="keyword">auto</span> result = allContributions(front);</div>
<div class="line"><a id="l00368" name="l00368"></a><span class="lineno">  368</span>        result.erase(result.begin(),result.end()-k);</div>
<div class="line"><a id="l00369" name="l00369"></a><span class="lineno">  369</span>        std::reverse(result.begin(),result.end());</div>
<div class="line"><a id="l00370" name="l00370"></a><span class="lineno">  370</span>        <span class="keywordflow">return</span> result;</div>
<div class="line"><a id="l00371" name="l00371"></a><span class="lineno">  371</span>    }</div>
</div>
<div class="line"><a id="l00372" name="l00372"></a><span class="lineno">  372</span>    </div>
<div class="line"><a id="l00373" name="l00373"></a><span class="lineno">  373</span>    <span class="comment"></span></div>
<div class="line"><a id="l00374" name="l00374"></a><span class="lineno">  374</span><span class="comment">    /// \brief Returns the index of the points with largest contribution as well as their contribution.</span></div>
<div class="line"><a id="l00375" name="l00375"></a><span class="lineno">  375</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00376" name="l00376"></a><span class="lineno">  376</span><span class="comment">    /// As no reference point is given, the extremum points can not be computed and are never selected.</span></div>
<div class="line"><a id="l00377" name="l00377"></a><span class="lineno">  377</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00378" name="l00378"></a><span class="lineno">  378</span><span class="comment">    /// \param [in] points The set \f$S\f$ of points from which to select the largest contributor.</span></div>
<div class="line"><a id="l00379" name="l00379"></a><span class="lineno">  379</span><span class="comment">    /// \param [in] k The number of points to select.</span></div>
<div class="line"><a id="l00380" name="l00380"></a><span class="lineno">  380</span><span class="comment"></span>    <span class="keyword">template</span>&lt;<span class="keyword">class</span> Set&gt;</div>
<div class="foldopen" id="foldopen00381" data-start="{" data-end="}">
<div class="line"><a id="l00381" name="l00381"></a><span class="lineno"><a class="line" href="structshark_1_1_hypervolume_contribution3_d.html#a62366c7be907e3f5e409b010970e2913">  381</a></span>    std::vector&lt;KeyValuePair&lt;double,std::size_t&gt; &gt; <a class="code hl_function" href="structshark_1_1_hypervolume_contribution3_d.html#a62366c7be907e3f5e409b010970e2913" title="Returns the index of the points with largest contribution as well as their contribution.">largest</a>(Set <span class="keyword">const</span>&amp; points, std::size_t k)<span class="keyword">const</span>{</div>
<div class="line"><a id="l00382" name="l00382"></a><span class="lineno">  382</span>        <a class="code hl_define" href="_exception_8h.html#adce1f80097c69010f5eab2618fa2e971">SHARK_RUNTIME_CHECK</a>(points.size() &gt;= k, <span class="stringliteral">&quot;There must be at least k points in the set&quot;</span>);</div>
<div class="line"><a id="l00383" name="l00383"></a><span class="lineno">  383</span>        <span class="comment">//reference point computation, and obtain the indizes of the extremum elements</span></div>
<div class="line"><a id="l00384" name="l00384"></a><span class="lineno">  384</span>        std::size_t minIndex[]={0,0,0};</div>
<div class="line"><a id="l00385" name="l00385"></a><span class="lineno">  385</span>        <span class="keywordtype">double</span> minVal[]={points[0](0),points[0](1),points[0](2)};</div>
<div class="line"><a id="l00386" name="l00386"></a><span class="lineno">  386</span>        <span class="keywordtype">double</span> ref[]={points[0](0),points[0](1),points[0](2)};</div>
<div class="line"><a id="l00387" name="l00387"></a><span class="lineno">  387</span>        <span class="keywordflow">for</span>(std::size_t i = 0; i != points.size(); ++i){</div>
<div class="line"><a id="l00388" name="l00388"></a><span class="lineno">  388</span>            <span class="keywordflow">for</span>(std::size_t j = 0; j != 3; ++j){</div>
<div class="line"><a id="l00389" name="l00389"></a><span class="lineno">  389</span>                <span class="keywordflow">if</span>(points[i](j)&lt; minVal[j]){</div>
<div class="line"><a id="l00390" name="l00390"></a><span class="lineno">  390</span>                    minVal[j] = points[i](j);</div>
<div class="line"><a id="l00391" name="l00391"></a><span class="lineno">  391</span>                    minIndex[j]=i;</div>
<div class="line"><a id="l00392" name="l00392"></a><span class="lineno">  392</span>                }</div>
<div class="line"><a id="l00393" name="l00393"></a><span class="lineno">  393</span>                ref[j] = std::max(ref[j],points[i](j));</div>
<div class="line"><a id="l00394" name="l00394"></a><span class="lineno">  394</span>            }</div>
<div class="line"><a id="l00395" name="l00395"></a><span class="lineno">  395</span>        }</div>
<div class="line"><a id="l00396" name="l00396"></a><span class="lineno">  396</span>        </div>
<div class="line"><a id="l00397" name="l00397"></a><span class="lineno">  397</span>        </div>
<div class="line"><a id="l00398" name="l00398"></a><span class="lineno">  398</span>        std::vector&lt;Point&gt; front;</div>
<div class="line"><a id="l00399" name="l00399"></a><span class="lineno">  399</span>        <span class="keywordflow">for</span>(std::size_t i = 0; i != points.size(); ++i){</div>
<div class="line"><a id="l00400" name="l00400"></a><span class="lineno">  400</span>            front.emplace_back(points[i](0)-ref[0],points[i](1)-ref[1],points[i](2)-ref[2],i);</div>
<div class="line"><a id="l00401" name="l00401"></a><span class="lineno">  401</span>        }</div>
<div class="line"><a id="l00402" name="l00402"></a><span class="lineno">  402</span>        std::sort(</div>
<div class="line"><a id="l00403" name="l00403"></a><span class="lineno">  403</span>            front.begin(),front.end(),</div>
<div class="line"><a id="l00404" name="l00404"></a><span class="lineno">  404</span>            [](Point <span class="keyword">const</span>&amp; lhs, Point <span class="keyword">const</span>&amp; rhs){</div>
<div class="line"><a id="l00405" name="l00405"></a><span class="lineno">  405</span>                return lhs.f3 &lt; rhs.f3;</div>
<div class="line"><a id="l00406" name="l00406"></a><span class="lineno">  406</span>            }</div>
<div class="line"><a id="l00407" name="l00407"></a><span class="lineno">  407</span>        );</div>
<div class="line"><a id="l00408" name="l00408"></a><span class="lineno">  408</span>        </div>
<div class="line"><a id="l00409" name="l00409"></a><span class="lineno">  409</span>        <span class="keyword">auto</span> result = allContributions(front);</div>
<div class="line"><a id="l00410" name="l00410"></a><span class="lineno">  410</span>        <span class="keywordflow">for</span>(std::size_t j = 0; j != 3; ++j){</div>
<div class="line"><a id="l00411" name="l00411"></a><span class="lineno">  411</span>            <span class="keyword">auto</span> pos = std::find_if(</div>
<div class="line"><a id="l00412" name="l00412"></a><span class="lineno">  412</span>                result.begin(),result.end(),</div>
<div class="line"><a id="l00413" name="l00413"></a><span class="lineno">  413</span>                [&amp;](<a class="code hl_struct" href="structshark_1_1_key_value_pair.html" title="Represents a Key-Value-Pair similar std::pair which is strictly ordered by it&#39;s key.">KeyValuePair&lt;double,std::size_t&gt;</a> <span class="keyword">const</span>&amp; p){</div>
<div class="line"><a id="l00414" name="l00414"></a><span class="lineno">  414</span>                    return p.value == minIndex[j];</div>
<div class="line"><a id="l00415" name="l00415"></a><span class="lineno">  415</span>                }</div>
<div class="line"><a id="l00416" name="l00416"></a><span class="lineno">  416</span>            );</div>
<div class="line"><a id="l00417" name="l00417"></a><span class="lineno">  417</span>            <span class="keywordflow">if</span>(pos != result.end())</div>
<div class="line"><a id="l00418" name="l00418"></a><span class="lineno">  418</span>                result.erase(pos);</div>
<div class="line"><a id="l00419" name="l00419"></a><span class="lineno">  419</span>        }</div>
<div class="line"><a id="l00420" name="l00420"></a><span class="lineno">  420</span>        <span class="keywordflow">if</span>(result.size() &gt; k)</div>
<div class="line"><a id="l00421" name="l00421"></a><span class="lineno">  421</span>            result.erase(result.begin(),result.end()-k);</div>
<div class="line"><a id="l00422" name="l00422"></a><span class="lineno">  422</span>        std::reverse(result.begin(),result.end());</div>
<div class="line"><a id="l00423" name="l00423"></a><span class="lineno">  423</span>        <span class="keywordflow">return</span> result;</div>
<div class="line"><a id="l00424" name="l00424"></a><span class="lineno">  424</span>    }</div>
</div>
<div class="line"><a id="l00425" name="l00425"></a><span class="lineno">  425</span>};</div>
</div>
<div class="line"><a id="l00426" name="l00426"></a><span class="lineno">  426</span> </div>
<div class="line"><a id="l00427" name="l00427"></a><span class="lineno">  427</span>}</div>
<div class="line"><a id="l00428" name="l00428"></a><span class="lineno">  428</span><span class="preprocessor">#endif</span></div>
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